Electron Propagation in RHESSI flares
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Electron Propagation in RHESSI flares
Markus J. Aschwanden (LMSAL)
5th General RHESSI Workshop, Locarno, Switzerland, 7-11 June 2005Group 1 : Electron Acceleration and Propagation
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Analysis of energy-dependent hard X-ray time delays:
1) Electron time-of-flight distance from dt/dE<02) Electron density in coronal trap from dt/dE>03) Neupert effect from dt/dE (E<15 keV)4) Proton speed from (dt_e-dt_p)/dE
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Electron velocityDispersion:
21 v
l
v
lt TOFTOFprop
Pitch angle:
v
vlll TOFTOFmag
||)cos(
Magnetic twist:
)cos(magloop ll Electron energy:
2
2
)/(1
1
cvcme
Photon energy:
eHXRE (Bremsstrahlung cross-section)
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Electron time-of-flightmeasurements enable thelocalization of the acceleration region.
Aschwanden (2002)
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Previous TOF measurementsfrom CGRO and Yohkoh:
L_TOF/h_loop = 1.40.3Aschwanden et al. (1996)
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Previous TOF measurementsfrom CGRO and Yohkoh:L_TOF/h_loop = 1.40.3
Aschwanden et al. (1996)
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Can we reproduce electron time-of-flight measurementswith comparable accuracy from RHESSI as from CGRO ?
Problems:
1) Reduced sensitivity due to smaller detector area (9*40/2=180 cm^2 for RHESSI vs. 2000*4*cos(45)=5600 cm^2 for BATSE/CGRO) 5600/180=30 x less sensitivity sqrt(30)=5.5 larger uncertainties in timing
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Can we reproduce electron time-of-flight measurementswith comparable accuracy from RHESSI as from CGRO ?
Problems:
2) Demodulation of high-resolution time profiles introduces additional data noise and artifact residuals.
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2-s highpass-filtered demodulated time profiles
Residuals fromdemodulation algorithmwith periods of ~1.8 s
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4-s highpass-filtered demodulated time profiles
Residuals fromdemodulation algorithmwith periods of ~2.7 s
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8-s highpass-filtered demodulated time profiles
Residuals fromdemodulation algorithmwith periods of ~2.7 s
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Residuals from demodulation algorithm prevent analysis of highpass-filtered data TOF measurements not feasible with RHESSI data
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Analysis of energy-dependent hard X-ray time delays:
1) Electron time-of-flight distance from dt/dE<02) Electron density in coronal trap from dt/dE>03) Neupert effect from dt/dE (E<15 keV)4) Proton speed from (dt_e-dt_p)/dE
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Generally, the HXR pulses or fine structure show TOF delays,while the lowpass-filtered flux shows delays of opposite sign (trapping)
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Weak-diffusion trapping model:Trapping time is given byCollisional deflection time:
ln
201095.0
2/38
e
keVdefltrap ntt
Coulomb logarithm:
)](100.8ln[ln 2/16 eenT
Photon energy:
eHXRE (Bremsstrahlung cross-section)
2/3)( EEt
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Highpass-filtered HXR time pulses Injection profileLowpass-filtered HXR time profile Trap-precipitating fluxObserved time profile in HXR:= convolution of direct-precipitation and trapped-precipitation
'])(
)'(exp[)',(
)1(),(),(
0
dtt
tttf
t
qtfqtf
t
traptrap
precinjprec
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(Schmahl & Hurford 2002) single source
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Spectral variation of 2 subsequent loops Noise due to demodulation residuals
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Krucker & Lin (2002)
Lowpass-filtered time profile contains multiple loops with different timing
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(Schmahl & Hurford 2002; Wang et al. 2002)
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(Saint-Hilaire & Benz 2002; Schmahl & Hurford 2002)
Spectral variation at >20 keVNeupert effect <20 keV
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Alexander & Metcalf (2002)Fletcher & Hudson (2002)Krucker & Lin (2002)
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Results:
# Date Start GOES Density Energy [UT] class log(n_e) E[keV]1) 2002-Feb-20 09:58 M4.3 11.2+1.5 15-35 2) 2002-Feb-20 11:07 C7.5 … pulse overlap3) 2002-Feb-20 21:10 M2.4 11.0+0.2 25-404) 2002-Feb-26 10:26 C9.6 … pulse overlap5) 2002-Mar-14 01:41 M5.7 … incomplete data6) 2002-Mar-17 19:26 M4.0 11.7+0.1 25-60 10.5+0.1 15-607) 2002-Mar-18 19:15 C8.9 10.6+0.3 15-25 10.2+0.1 15-3020) 2002-Jun-02 11:44 M1.0 11.5+0.1 20-60 11.4+0.1 20-6023) 2002-Jul-23 00:00 X4.8 11.6+0.2 35-60
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Comparision with electron densities obtained from CCGRO and Yohkoh
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Comparision with electron densities obtained from CCGRO and Yohkoh
RHESSI
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Conclusions :1) Electron time-of-flight measurements cannot be carried out with current RHESSI demodulation algorithm (modulation residuals).
2) Energy-dependent HXR delays of lowpass-filtered (>4 s) RHESSI time profiles in the energy range of ~15-60 keV show delays that are consistent with a trap-plus-precipitation model with a timing of t(E)~E^3/2.
3) The resulting trap densities are found in the range of log(n_e [cm^-3])=10.2-11.7 and are consistent with CGRO data (obtained with the same technique) and with Yohkoh/SXT data (obtained from EM and loop geometry).
4) In 3 out of 9 flares trap densities could not be evaluated, most likely because subsequent HXR pulses with different spectra cannot be separated on >4s time scales.
5) The obtained trap densities can be used to model coronal HXR emission in Masuda-Sui-Holman-type sources.